Your analysis is partially true.
First, international trade is conducted is US$ that is why forex is based with the US$. Looking from the japanese point of view, the manufacturer of say, lens, has its cost structure in Yen. Because it is in Japan, only japanese yen matters to him. No body in Japan cares about US$ or korean won. Now the Japanese want to sell a lens at Yen10,000.People in Japan pays Yen 10,000 the manufacturer receives the amount in Yen.
Now a foreigner who wants the lens will need to buy japanese yen to pay the seller who only want yen. Assuming (the exchange rate here is for illustration only) at an exchange rate of US$1 to Y200 the foreigner will need US$50 to buy Yen10,000 to pay for the lens. When the yen weakens to say USD1 to Yen250 the foreigner will need US$40 to pay for the same lens. The result is that the japanese still receives his Y10,000 for the lens, but foreigners pay less. Therefore it is cheaper to buy japanese product when japanese weakens i.e prices must fall.
Secondly, when a country weakens its currency it is hoped that a decrease in price (through elasticity of demand) will induce a large increase in demand from other countries..but this is not our concern.
My conclusion is prices will fall with a weaken yen. It is a matter of time.